Download 2.2 Conditional Statements

Name ___________________________________________ Date _____________________ Class ____________________
2.2 Conditional Statements
Unit 1: Foundations for Geometry
A conditional statement is a statement that can be written as an if-then statement,
“if p, then q.”
The hypothesis comes
after the word if.
The conclusion comes
after the word then.
Sometimes it is necessary to rewrite a conditional statement so that it is in if-then form.
Conditional:
A person who practices putting will improve her golf game.
If-Then Form:
If a person practices putting, then she will improve her golf game.
For each conditional, circle the hypothesis and underline the conclusion.
1. If x is an even number, then x is divisible by 2.
2. The circumference of a circle is 5π inches if the diameter of the circle is 5 inches.
3. If a line containing the points J, K, and L lies in plane P then J, K, and L are coplanar.
Write a conditional statement from each given statement.
4. Congruent segments have equal measures.
_________________________________________________________________________________________________
5. On Tuesday, play practice is at 6:00.
_________________________________________________________________________________________________
Determine whether the following conditional is true. If false, give a counterexample.
6. If two angles are supplementary, then they form a linear pair.
_________________________________________________________________________________________________
Match the correct term to complete each sentence.
7. A conditional statement is a statement that can be written
in the form “_______ p, _______ q.”
8. The __________ is the part p of a conditional statement
following the word if.
A. hypothesis
9. The __________ is the part q of a conditional statement
following the word then.
C. conclusion
10. The __________ is the statement formed by negating the
hypothesis and the conclusion.
11. The __________ is the statement formed by exchanging the
hypothesis and the conclusion.
B. converse
D. if; then
E. inverse
F. negating; switching
12. The contrapositive is the statement formed by both
__________ and __________ the hypothesis and the conclusion.
Holt McDougal Geometry
The negation of a statement, “not p,” has the opposite truth value of the original statement.
Statement
Conditional
Truth
Value
Example
H
C
True
If a figure is a square, then it has four right angles.
Converse:
Switch H and C.
Inverse:
Negate H and C.
Contrapositive:
Switch and
negate H and C.
If a figure has four right angles, then it is a square.
If a figure is not a square, then it does not have four right angles.
If a figure does not have four right angles, then it is not a square.
False
False
True
Use the following conditional statement for #13–18: If it is a bicycle, then it has two wheels.
13. What is the hypothesis of the conditional statement?
______________________________
14. What is the conclusion of the conditional statement?
______________________________
15. “If it has two wheels, then it is a bicycle.” Is this the
converse, the inverse, or the contrapositive?
______________________________
16. “If it does not have two wheels, then it is not a bicycle.”
Is this is the converse, the inverse, or the contrapositive? ______________________________
17. “If it is not a bicycle, then it does not have two wheels.”
Is this is the converse, the inverse, or the contrapositive? ______________________________
18. Which of the original statements, the converse, the inverse, and the contrapositive, are true
statements? (Hint: Can you think of another two-wheeled vehicle?)
_________________________________________________________________________________________________
Write the converse, inverse, and contrapositive of each conditional statement and find the
truth value of each.
19. If an animal is an armadillo, then it is nocturnal.
_________________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
20. If an angle has a measure less than 90°, then it is acute.
_________________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________